Exclusive group - I left organisation of alumni getting it set up (10)

I believe the answer is:

illuminati

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'exclusive group i left organisation of alumni getting it set up' is the definition.
I can't tell whether this defines the answer.

'i left organisation of alumni getting it set up' is the wordplay.
'left' becomes 'l' (common abbreviation).
'organisation of' is an anagram indicator (I've seen 'organisation' mean this).
'getting' is a charade indicator (letters next to each other).
'set up' says the letters should be written in reverse (in a down clue, letters go up).
'it' back-to-front is 'ti'.
'alumni' is an anagram of 'lumina'.
'i'+'l'+'lumina'+'ti'='ILLUMINATI'

Can you help me to learn more?

(Other definitions for illuminati that I've seen before include "Claimers of special knowledge" , "clever people" .)

I've seen this clue in The Independent.

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